Author
Akihiro Nozaki
Bio: Akihiro Nozaki is an academic researcher from University of Yamanashi. The author has contributed to research in topics: Deterministic finite automaton & Randomness. The author has an hindex of 2, co-authored 4 publications receiving 13 citations.
Papers
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TL;DR: A series-parallel decomposition of an automaton A into r components is said to be practical if every component has fewer states than the original automaton C iff the product of the numbers of states of components is equal to the number ofStates of A.
Abstract: A series-parallel decomposition of an automaton A into r components ( r ⩾ 1) is said to be practical if every component has fewer states than the original automaton A . It is said to be perfect iff the product of the numbers of states of components is equal to the number of states of A . Necessary and sufficient conditions are given for a Moore-type automaton to have a practical decomposition. An algebraic criterion is also given for a reduced, strongly connected permutation automaton to have a perfect decomposition. It should be noted that an automaton may have a perfect decomposition although its semigroup is a simple group, and that an automaton may not have a practical decomposition, while its semigroup is a nonsimple group.
7 citations
TL;DR: It is shown that the optimal bound to the lengths of input strings to be examined for checking equivalence of non-deterministic automata is of order O (2 m + 2 n ), where m and n are the state numbers of the automata under question.
5 citations
TL;DR: Here proposed are complexity measures of finite sequences of symbols, based on finite automata, defined and characterized using ultimately periodic sequences, and a refined measure, F-complexity, introduced, showing that highly random sequences have large F- complexities, but the converse is not always true.
Abstract: Here proposed are complexity measures of finite sequences of symbols, based on finite automata. Basic properties of these measures are demonstrated. The relation between the complexity for generating a sequence and the randomness of the generated sequence is also discussed. First, the notion of A-complexity is defined and characterized using ultimately periodic sequences (Theorem 1). A refined measure, F-complexity, is then introduced. It is shown that highly random sequences have large F-complexities (Theorem 2), but the converse is not always true (Theorem 3). Finally, the c-complexity is proposed to remedy this shortcoming of F-complexity. It includes as special cases both A-complexity and F-complexity. It is shown that certain sequences with high c-complexities, complete periodic sequences, are equidistributed (Theorem 4).
1 citations
TL;DR: It is shown that a ''parallelizable'' asynchronous circuit is hazard free iff so it is in its synchronous move and the class of parallelizable circuits contains properly theclass of semimodular circuits.
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01 Jan 1980
TL;DR: The aim of this chapter is to introduce the reader to the theory of discrete information processing systems (automata) and to develop an algebraic framework within which to talk about their complexity.
Abstract: Much scientific work today is directed towards understanding complexity — the complexity of numerical algorithms, of the English syntax, of living organisms or ecological systems, to cite only a few examples. The aim of this chapter is to introduce the reader to the theory of discrete information processing systems (automata) and to develop an algebraic framework within which we can talk about their complexity.
124 citations
TL;DR: The specification discloses wheel and axle assemblies in each of which a sealing washer serves both as a bearing seal and a thrust washer.
55 citations
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TL;DR: The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length ≤ n (by accepting one and rejecting the other) as discussed by the authors, which is known as the separating word problem.
Abstract: The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem, consider some variations, and prove several new results.
20 citations
TL;DR: It is shown that an NGSMM with finite length-degree can be effectively decomposed into finitely many NGSMsM1, ...,MN having length- Degree at most 1 such that the transduction realized byM is the union of the transductions realized by M1,...,MN.
Abstract: We investigate finite transducers and their inner structure with regard to the lengths of values. Our transducer models are the normalized finite transducer (NFT) and the nondeterministic generalized sequential machine (NGSM), which is a real-time NFT. The length-degree of an NFT is defined to be the maximal number of different lengths of values for an input word or is infinite, depending on whether or not a maximum exists. We show: An NGSMM with finite length-degree can be effectively decomposed into finitely many NGSMsM1, ...,MN having length-degree at most 1 such that the transduction realized byM is the union of the transductions realized byM1, ...,MN. Using this decomposition, the equivalence of NGSMs with finite length-degree is recursively decidable. Whether or not an NGSM has finite length-degree can be decided in deterministic polynomial time. By reduction, all these results can be generalized to NFTs.
15 citations
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TL;DR: In this article, the cascade product of permutation groups is defined as an external product, an explicit construction of substructures of the iterated wreath product that are much smaller than the full Wreath product.
Abstract: We define the cascade product of permutation groups as an external product, an explicit construction of substructures of the iterated wreath product that are much smaller than the full wreath product. This construction is essential for computational implementations of algebraic hierarchical decompositions of finite automata. We show how direct, semidirect, and wreath products and group extensions can all be expressed as cascade products, and analyse examples of groups that can be constructed isomorphically by this generic extension giving them a hierarchically coordinatized form.
11 citations